In our previous works on the XXZ chain of spin one half, we have studied the problem of constructing a basis of local operators whose members have simple vacuum expectation values. For this purpose a pair of fermionic creation operators have been int
roduced. In this article we extend this construction to the spin one case. We formulate the fusion procedure for the creation operators, and find a triplet of bosonic as well as two pairs of fermionic creation operators. We show that the resulting basis of local operators satisfies the dual reduced qKZ equation.
Extending our previous construction in the sine-Gordon model, we show how to introduce two kinds of fermionic screening operators, in close analogy with conformal field theory with c<1.
We study one-point functions of the sine-Gordon model on a cylinder. Our approach is based on a fermionic description of the space of descendent fields, developed in our previous works for conformal field theory and the sine-Gordon model on the plane
. In the present paper we make an essential addition by giving a connection between various primary fields in terms of yet another kind of fermions. The one-point functions of primary fields and descendants are expressed in terms of a single function defined via the data from the thermodynamic Bethe Ansatz equations.
The Grassmann structure of the critical XXZ spin chain is studied in the limit to conformal field theory. A new description of Virasoro Verma modules is proposed in terms of Zamolodchikovs integrals of motion and two families of fermionic creation op
erators. The exact relation to the usual Virasoro description is found up to level 6.
